Effect sizes based on summary statistics

When you have summary statistics but not the underlying data, as you
might when reading a journal article, you can use Stata's immediate
command. Let's pretend our birthweight example was published.
The hypothetical article recorded that for the 115 mothers who did
not smoke, the average birthweight was 3,054.957 grams (sd=752.409)
and that for the 74 smokers, the average was 2772.297 grams (sd=659.8075). We type

We can obtain the proportion of variability explained (effect
sizes) measured by η2 or ω2. Here is the
default η2 measure:

. estat esize
Effect sizes for linear models

Source

Eta-Squared df [95% Conf. Interval]

Model

.0471158 3 0 .1062782

smoke

.033257 1 .0014433 .0975557

drvisit

.006391 1 0 .0474531

c.smoke#c.drvisit

.0026012 1 0 .0361357

Reported are full and partial η2 values along with their
confidence intervals. We would have obtained similar output
had we requested the ω2 measure.

Effect sizes for linear models (proportion of variability explained)

We can also use the estat esize postestimation command to calculate
effect sizes after fitting linear models.

We replace the insignificant drvisit variable with the continuous
variable age and fit the model using linear regression.

. regress bwt smoke##c.age

Source

SS df MS

Number of obs = 189

F( 3, 185) = 4.55

Model

6859112.22 3 2286370.74

Prob > F = 0.0042

Residual

93056186.4 185 503006.413

R-squared = 0.0686

Adj R-squared = 0.0535

Total

99915298.6 188 531464.354

Root MSE = 709.23

bwt

Coef. Std. Err. t P>|t| [95% Conf. Interval]

smoke

smoker

797.9369 484.3249 1.65 0.101 -157.5731 1753.447

age

27.60058 12.14868 2.27 0.024 3.632806 51.56835

smoke#c.age

smoker

-46.51558 20.44641 -2.28 0.024 -86.85368 -6.177479

_cons

2408.383 292.1796 8.24 0.000 1831.951 2984.815

This time, we request the ω2 estimates of effect size:

. estat esize, omega
Effect sizes for linear models

Source

Omega-Squared df [95% Conf. Interval]

Model

.0535463 3 0 .1223273

smoke

.0091327 1 0 .0601797

age

0 1 0 .0231396

c.smoke#c.age

.0219567 1 0 .0829855

Reported are full and partial ω2 values.

ANOVA and regression effect sizes from summary statistics

If we did not have the data to estimate this model but instead
found the regression fit published in a journal, we could still
estimate the overall η2 and ω2 from the model's
degrees of freedom and the summary statistic that F(3, 185) = 4.55.
We could type

. esizei 3 185 4.55
Effect sizes for linear models

Effect Size

Estimate [95% Conf. Interval]

Eta-Squared

.0687138 .0079234 .1364187

Omega-Squared

.0536119 0 .1224147

The η2 agrees to three decimal places. Had we typed
4.5454107 rather than 4.55, we would have had full agreement to
the shown eight decimal places.